Well yes, nobody is contesting counter-steering.
The scene you are describing is from "Twist of the Wrist 2" movie. I have it on my phone actually, I watch it from time to time on a train, when not commuting on my bike.
So yes, that scene basically shows that "body steering" is not efficient enough to move the bike into a turn.
It still affects the bike's direction, but counter-steering is the main mode to control the bike. So that is established and done with.
Additional movement on the bike, simply add TO the counter-steering, be that to tighten the turn, to balance the bike or to increase/decrease lean angle. ALL of that is complimentary to counter-steering.
Harvey: yes, very often I feel frozen on the bars. One hand pushing one way and the other, opposite. It usually happens when I'm going beyond my comfort / skill limit and I tighten on the bars. I am fully aware of it mentally in my head, WHILE doing it, but its extremely hard to get my body to do what my conscious mind wants.
It is bizarre, sort of an out of body experience, where hands are doing what you do NOT want them to do, and you can't do anything about it.